What is Parallel Combination of Resistors?

S6-SA3-0202

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

When two or more resistors are connected across the same two points in a circuit, such that the current has multiple paths to flow, they are said to be in parallel combination. In this arrangement, the voltage across each resistor is the same, but the current divides among them.

Simple Example

Quick Example

Imagine you have three roads connecting your home to the market. If you can choose any one of these roads to reach the market, and all roads start and end at the same two points (your home and the market), they are like resistors in parallel. The traffic (current) will divide among the roads, but the 'distance' (voltage) between your home and the market remains the same for all roads.

Worked Example

Step-by-Step

QUESTION: Three resistors with resistances R1 = 6 ohm, R2 = 3 ohm, and R3 = 2 ohm are connected in parallel. Calculate their equivalent resistance.

STEP 1: Write down the formula for equivalent resistance in a parallel combination.
1/R_eq = 1/R1 + 1/R2 + 1/R3
---STEP 2: Substitute the given values into the formula.
1/R_eq = 1/6 + 1/3 + 1/2
---STEP 3: Find a common denominator for the fractions. The least common multiple of 6, 3, and 2 is 6.
1/R_eq = 1/6 + (1*2)/(3*2) + (1*3)/(2*3)
---STEP 4: Simplify the fractions.
1/R_eq = 1/6 + 2/6 + 3/6
---STEP 5: Add the fractions.
1/R_eq = (1 + 2 + 3) / 6
1/R_eq = 6/6
1/R_eq = 1
---STEP 6: To find R_eq, take the reciprocal of the result.
R_eq = 1/1
R_eq = 1 ohm

ANSWER: The equivalent resistance of the three resistors connected in parallel is 1 ohm.

Why It Matters

Understanding parallel combinations is crucial for designing efficient electrical circuits, from your home wiring to complex computer chips. Electrical engineers use this to ensure devices get the right power, and even AI/ML systems running on powerful servers rely on circuits designed using these principles to manage power effectively.

Common Mistakes

MISTAKE: Adding resistances directly as R_eq = R1 + R2 + R3 | CORRECTION: Remember that for parallel combinations, you add the reciprocals of resistances (1/R_eq = 1/R1 + 1/R2 + ...) and then take the reciprocal of the final sum.

MISTAKE: Forgetting to take the reciprocal at the end, leaving the answer as 1/R_eq instead of R_eq | CORRECTION: Always remember the last step: if you calculate 1/R_eq, your final answer for R_eq is 1 divided by that value.

MISTAKE: Confusing the formulas for series and parallel combinations | CORRECTION: In parallel, voltage is the same across each resistor and current divides. In series, current is the same, and voltage divides. This helps you remember which formula to use.

Practice Questions

Try It Yourself

QUESTION: Two resistors, 10 ohm and 15 ohm, are connected in parallel. What is their equivalent resistance? | ANSWER: 6 ohm

QUESTION: A circuit has four resistors in parallel: 4 ohm, 8 ohm, 12 ohm, and 24 ohm. Find the equivalent resistance. | ANSWER: 2 ohm

QUESTION: If two resistors connected in parallel have an equivalent resistance of 4 ohm, and one of the resistors is 12 ohm, what is the resistance of the other resistor? | ANSWER: 6 ohm

MCQ

Quick Quiz

When resistors are connected in parallel, which of the following statements is TRUE?

The current is the same through each resistor.

The voltage across each resistor is the same.

The equivalent resistance is greater than the largest individual resistance.

The total resistance is the sum of individual resistances.

The Correct Answer Is:

In a parallel combination, all components are connected across the same two points, meaning they share the same potential difference or voltage. Current divides among the paths, and the equivalent resistance is always less than the smallest individual resistance.

Real World Connection

In the Real World

Think about the electrical wiring in your home. All the lights, fans, and appliances are connected in parallel to the main power supply. This ensures that each appliance gets the full 220V (or 110V in some regions) it needs to operate, and if one appliance breaks or is switched off, the others continue to work without interruption.

Key Vocabulary

Key Terms

RESISTOR: An electronic component that opposes the flow of electric current | PARALLEL COMBINATION: An arrangement where components are connected across the same two points, sharing the same voltage | EQUIVALENT RESISTANCE: The single resistance that can replace a combination of resistors without changing the total current or voltage in the circuit | VOLTAGE: The electrical potential difference between two points in a circuit | CURRENT: The flow of electric charge per unit time

What's Next

What to Learn Next

Great job understanding parallel combinations! Next, you should explore 'Series Combination of Resistors' to see how components behave differently when connected end-to-end. Then, you can learn about 'Mixed Grouping of Resistors' to combine both concepts and solve more complex circuit problems.